Question: $a_n={\dfrac{9^n}{(n+1)2^{2n-1}}}$ 1) Find $\lim_{n\to\infty}\left| \dfrac{a_{n+1}}{a_n} \right|$. $\lim_{n\to\infty}\left|\, \frac{{{a}_{n+1}}}{{{a}_{n}}} \,\right|=$
Solution: $\lim_{n\to\infty}\left| \,\frac{{{a}_{n+1}}}{{{a}_{n}}} \,\right|=\dfrac{9}{4}$ Since the limit, $\dfrac{9}{4}$, is greater than $1$, the ratio rest tells us that the series diverges.